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The spectrum observed by the Pierre Auger experiment, shown by filled squares in figure 4, differs from the HiRes and TA spectra, shown by triangles and circles. On the other hand, as discussed in the previous section, the HiRes/TA data are well fitted by the pair-production dip, shown as continuos line in figure 4.

Figure 4

Figure 4. Spectrum of UHECR as observed by HiRes, TA and Auger experiments (as labeled). Continuos line is the best fit of HiRes/TA with a pure proton composition (dip model).

In the framework of the dip model, taking into account the systematic errors in energy determination, one can try to shift the Auger energy scale having the dip behavior as reference. This procedure, proposed in [1], is based on the fact that the energy position of the pair-production dip is rigidly fixed by the interaction of protons with the CMB radiation field, so that it can be used as a "standard candle". This approach is based on a single hypothesis: a pure proton composition of UHECR.

Shifting accordingly to the dip "standard candle" the energy scale of the Auger data one has the result shown in figure 5. Where the Auger data have been shifted according to EkcalE with kcal = 1.22, allowed by the systematic error claimed by the Auger collaboration [7].

After the energy shift, the apparent coincidence of the Auger and HiRes/TA data is mainly related to the low energy part of the spectra (see figure 5), while at the highest energies statistical uncertainties are too large to distinguish among spectra. Nevertheless, while HiRes and TA data are compatible with the GZK steepening the Auger data, which at energies around 50 EeV still show low statistical errors, are not compatible with the behavior expected from the photo-pion production process of protons on the CMB field.

Figure 5

Figure 5. The same as in 4 with the Auger spectrum shifted in energy as EkcalE with kcal = 1.22.

Even playing with the different parameters involved in the computation (i.e. injection power law index gammag, sources cosmological evolution, maximum acceleration energy, local over-density of sources, etc.) one could not reconcile the Auger spectrum behavior with the GZK expectation. Being the GZK steepening a clear signal of a proton dominated spectrum, the Auger spectrum is coherent with the chemical composition measured by this experiment at the highest energies which is quite incompatible with a pure proton composition. Auger data on chemical composition show a steady behavior that, starting already from energies around 3 EeV, moves from a light (proton) to an heavier composition reaching an almost pure Iron composition at energies around 30 EeV [7]. These observations based on the Auger Fluorescence Detector (FD) are further straightened by the observations of the Auger Surface Detector (SD), namely the shower muon content and the signal rise time in the Cherenkov tanks [8].

The early steepening observed in the Auger spectrum can be easily explained in terms of nuclei propagation. Nevertheless, even assuming a rich chemical composition with different nuclei species injected at the source it is not easy to obtain a good explanation of both spectrum and chemical composition observed by Auger. A wide class of mixed composition models [9], while showing a good description of the spectrum, fail to fit the mass composition observed by Auger. Most of these models assume a mass composition similar to the one observed at galactic scales, therefore enhanced in protons, and the resulting mass composition starts to become heavier only at energies E > 50 EeV [9] where photo-pion production substantially depletes the proton component.

At the galactic energy scales, the mass composition becoming heavier with increasing energy appears as a natural consequence of the rigidity dependent scenario for particles acceleration. The maximum acceleration energy that a single specie can reach is proportional to the particles charge EmaxZ = Z Emaxp and the contribution to the spectrum at these energies of particles with charge lower than Z is suppressed. The disappointing model for UHECR [13] was build exactly under such assumption on maximum energy. In [13] was demonstrated that to avoid a proton dominated spectrum at the highest energies one must assume that the maximum energy for protons is in the range 4-10 EeV. This conclusion remains valid for a large range of generation power law indexes gammag ≃ 2.0-2.8, nevertheless to achieve a good description of the observed UHECR spectrum in the disappointing model one should assume a quite flat injection spectrum with gammag = 2.0-2.2.

This fact, as we will discuss in the next session, has important consequences on the transition between galactic and extra-galactic CR. In figures 6, 7 we plot two different implementations of the disappointing model: a simple two component model with protons and iron (figure 6), the same two components model with a diffusion cut-off in the iron spectrum due to the possible presence of a nG scale intergalactic magnetic field (figure 7). Note that the gap in the spectrum in figure 7 can be filled by the presence of secondary nuclei produced by the photo-disintegration of iron.

Figure 6

Figure 6. Energy spectrum in the two components model with proton and iron nuclei for a homogeneous distribution of sources with gammag = 2.0 and Emaxp = 4 EeV.

This model was called "disappointing" because it corresponds to a lack of many signatures predicted in the alternative case of a proton dominated scenario, such as the cosmogenic neutrino production and correlation with astrophysical sources. The disappointing model as presented here and in [13] is not complete because, while it reaches a good description of the observed Auger spectrum, it does not try to describe also the chemical composition observed at all energies.

Figure 7

Figure 7. As in figure 6 with a diffusion cut-off, the gap is expected to be filled by intermediate mass nuclei.

The only successful theoretical attempt to fit at once spectrum and chemical composition of Auger was presented in [14] where it is assumed the presence of a very nearby source (≃ 70 Mpc) with a very flat generation spectrum (gammag ≃ 1.6) injecting heavy nuclei only.

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